Principal component analyses

Methods:

Principal component analyses (PCA) (function prcomp) of scaled and centered physiological parameters (host carbohydrate, host lipid, host protein, algal endosymbiont chlorophyll a, algal endosymbiont cell density, holobiont calcification rate as previously for the same samples in Bove et al. (2019)) were employed to assess the relationship between physiological parameters and treatment conditions for each coral species. Main effects (temperature, pCO2, and reef environment) were evaluated using the adonis2 function (Tables XXX). All statistical analyses were performed in R (R version 3.6.3 (2020-02-29)) (R Core Development Team 2016).

Siderastrea siderea

## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 2000
## 
## adonis2(formula = sid_pca_df ~ fpco2 + ftemp + reef, data = s_df, permutations = bootnum, method = "eu")
##          Df SumOfSqs      R2       F    Pr(>F)    
## fpco2     3   150243 0.27232 11.4516 0.0004998 ***
## ftemp     1    24935 0.04520  5.7018 0.0039980 ** 
## reef      1    26681 0.04836  6.1009 0.0044978 ** 
## Residual 80   349861 0.63413                      
## Total    85   551720 1.00000                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Pseudodiploria strigosa

## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 2000
## 
## adonis2(formula = dip_pca_df ~ reef + fpco2 + ftemp, data = p_df, permutations = bootnum, method = "eu")
##          Df SumOfSqs      R2       F    Pr(>F)    
## reef      1   162037 0.07959 10.9355 0.0009995 ***
## fpco2     3   196323 0.09644  4.4165 0.0034983 ** 
## ftemp     1   625389 0.30720 42.2061 0.0004998 ***
## Residual 71  1052041 0.51677                      
## Total    76  2035789 1.00000                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Porites astreoides

## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 2000
## 
## adonis2(formula = por_pca_df ~ reef + ftemp + fpco2, data = a_df, permutations = bootnum, method = "eu")
##          Df SumOfSqs      R2       F    Pr(>F)    
## reef      1      505 0.00150  0.1692 0.8225887    
## ftemp     1    56228 0.16639 18.8252 0.0004998 ***
## fpco2     3    96015 0.28412 10.7153 0.0004998 ***
## Residual 62   185186 0.54799                      
## Total    67   337935 1.00000                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Figure 1

Figure 1. Principal component analyses (PCA) of all coral holobiont physiological parameters for S. siderea (A), P. strigosa (B), and P. astreoides (C) after 93 days of exposure to different temperature and pCO2 treatments. PCAs in the top row are depicted by temperature treatment for each species (28\(^\circ\) C blue; 31\(^\circ\) C red) and the bottom row of PCAs are depicted by pCO2 for each species (280 \(\mu\)atm light purple; 400 \(\mu\)atm dark purple; 700 \(\mu\)atm light orange; 2800 \(\mu\)atm dark orange). Arrows represent significant (p < 0.05) correlation vectors for physiological parameters and ellipses represent 95% confidence based on multivariate t-distributions.

Results:

Text for results of PCA will go here



Correlation assessments

Methods:

Text for methods of correlations will go here

## quartz_off_screen 
##                 2
## quartz_off_screen 
##                 2
## quartz_off_screen 
##                 2

Figure 2. Coral holobiont correlation matrices (bottom panel) and scatter plots (top panel) for S. siderea (A), P. strigosa (B), and P. astreoides (C) depicting pair-wise comparisons of physiological parameters within each species. Strength of correlations between parameteres is indicated by darker shades of blue in the bottom panel with a higher R2 value. Of these correlations, significant correlations are depicted with asterisks according to significance level (* p < 0.05; ** p < 0.01; *** p < 0.001). Scatter plots of physiological paramters are displayed in the top panel with temperature depicted by shape (28\(^\circ\) C filled points; 31\(^\circ\) C open points) and pCO2 depicted by colour (280 \(\mu\)atm light purple; 400 \(\mu\)atm dark purple; 700 \(\mu\)atm light orange; 2800 \(\mu\)atm dark orange)

Results:

Text for results of correlations will go here



Plasticity analyses

Methods:

Text for methods of plasticity will go here

S. siderea

## 
## Call:
## lm(formula = log(dist) ~ reef * (fpco2 + ftemp), data = sid_dist)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.78174 -0.31772  0.02219  0.36945  1.61358 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      0.18511    0.23659   0.782  0.43681    
## reefN            0.45572    0.35651   1.278  0.20569    
## fpco2420         0.74509    0.40498   1.840  0.07036 .  
## fpco2680         0.43093    0.29217   1.475  0.14506    
## fpco23300        1.09054    0.29810   3.658  0.00051 ***
## ftemp31          0.04848    0.23361   0.208  0.83626    
## reefN:fpco2420  -1.45153    0.55677  -2.607  0.01132 *  
## reefN:fpco2680  -1.00241    0.43178  -2.322  0.02340 *  
## reefN:fpco23300 -0.90776    0.42713  -2.125  0.03737 *  
## reefN:ftemp31   -0.05654    0.33833  -0.167  0.86780    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6702 on 65 degrees of freedom
## Multiple R-squared:  0.3277, Adjusted R-squared:  0.2346 
## F-statistic:  3.52 on 9 and 65 DF,  p-value: 0.001332

P. strigosa

## 
## Call:
## lm(formula = log(dist) ~ fpco2 * ftemp, data = dip_dist)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.80566 -0.39324 -0.02508  0.40695  1.45089 
## 
## Coefficients: (1 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        0.80474    0.15931   5.051  3.8e-06 ***
## fpco2420           0.21594    0.35545   0.608   0.5456    
## fpco2680          -0.19127    0.23321  -0.820   0.4151    
## fpco23300         -0.48076    0.22903  -2.099   0.0397 *  
## ftemp31           -0.20751    0.26552  -0.781   0.4374    
## fpco2420:ftemp31        NA         NA      NA       NA    
## fpco2680:ftemp31   0.02576    0.42512   0.061   0.9519    
## fpco23300:ftemp31  0.84383    0.38515   2.191   0.0320 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6373 on 65 degrees of freedom
## Multiple R-squared:  0.1064, Adjusted R-squared:  0.02391 
## F-statistic:  1.29 on 6 and 65 DF,  p-value: 0.2743

P. astreoides

## 
## Call:
## lm(formula = log(dist) ~ fpco2 + ftemp, data = por_dist)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6110 -0.3076  0.1067  0.3932  1.1107 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.56933    0.15308   3.719 0.000491 ***
## fpco2420    -0.20237    0.29678  -0.682 0.498332    
## fpco2680     0.04701    0.19656   0.239 0.811918    
## fpco23300    0.17055    0.20256   0.842 0.403651    
## ftemp31      0.30038    0.17213   1.745 0.086883 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5793 on 52 degrees of freedom
## Multiple R-squared:  0.06514,    Adjusted R-squared:  -0.006773 
## F-statistic: 0.9058 on 4 and 52 DF,  p-value: 0.4675

Figure 3

Figure 3. Text goes here for caption


Results:

Text for results of correlations will go here



Physiological paramters

Physiological response parameters were assessed using mixed-effects linear models across species and treatments. Model selection was carried out using backward elimination of random-effects followed by fixed-effects using the package lmerTest (version 3.1.3)

Protein

While value ~ species + fpco2 + ftemp + (1 | colony) + species:ftemp was the best-fit model structure identified, we wanted to model both pCO2 and temperature responses by species so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + (1 | colony)


Figure:

Carbohydrate

While value ~ species + ftemp was the best-fit model structure identified, we wanted to model responses with a random effect of colony so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + (1 | colony)


Figure:

Lipid

While value ~ species + ftemp + reef + species:ftemp + species:reef was the best-fit model structure identified, we wanted to model both pCO2 and temperature responses by species and with random effect of colony so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + reef + species:reef + (1 | colony)


Figure:

Density

While value ~ species + fpco2 + ftemp + reef + (1 | colony) + species:fpco2 + species:ftemp + fpco2:ftemp + species:reef + fpco2:reef + ftemp:reef + species:fpco2:ftemp + species:fpco2:reef + species:ftemp:reef + fpco2:ftemp:reef + species:fpco2:ftemp:reef was the best-fit model structure identified, we wanted to model both pCO2 and temperature responses by species and with random effect of colony so moving forward we are using the following model structure:

value ~ species * (fpco2 + ftemp) + reef + species:reef + (1 | colony)


Figure:

Chlorophyll

Since the best-fit model fits our design, we will proceed with the following model structure:

value ~ species + fpco2 + ftemp + reef + (1 | colony) + species:fpco2 + species:ftemp + fpco2:ftemp + species:reef


Figure:

Total Host

Since the best-fit model fits our design, we will proceed with the following model structure:

value ~ species + fpco2 + ftemp + reef + (1 | colony) + species:fpco2 + species:ftemp + species:reef + fpco2:reef + species:fpco2:reef


Figure:

Calcification

This is the same model from Bove et al 2019, just matching aesthetics for this manuscript.

Figure S1


Figure S1. Modeled 95% confidence interval of (A) host total protein (mg cm-2), (B) host total carbohydrate (mg cm-2), (C) host total lipid (mg cm-2), (D) cell density (106 cells cm-2), and (E) Chlorophyll a (ug cm-2) for S. siderea (left), P. strigosa (center), and P. astreoides (right) at T0 (green) or T90 (red/blue), with individual coral fragment physiology denoted by points. Blue denotes 28°C and red denotes 31°C, with pCO2 treatment along the x axis.



S. siderea gene expression subset

SSID subset PCA

## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 2000
## 
## adonis2(formula = s_df_sub[, c(14:17, 21:23, 29)] ~ fpco2 + fpco2:domSymb + domSymb + ftemp, data = s_df_sub, permutations = bootnum, method = "eu")
##               Df SumOfSqs      R2       F    Pr(>F)    
## fpco2          3    60040 0.26137 12.2655 0.0004998 ***
## domSymb        2    76699 0.33389 23.5033 0.0004998 ***
## ftemp          1    13933 0.06065  8.5391 0.0004998 ***
## fpco2:domSymb  6    28458 0.12389  2.9068 0.0029985 ** 
## Residual      31    50582 0.22020                      
## Total         43   229711 1.00000                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



Siderastrea siderea subset



Supplemental Tables

Table 1. T90 modeled mean coral host protein content and 95% confidence intervals for each species
treatment N mean lower 95% upper 95%
(a) SSID
300_28 11 0.54 0.47 0.60
300_31 9 0.48 0.41 0.55
3300_28 12 0.43 0.37 0.50
3300_31 12 0.38 0.31 0.44
420_28 12 0.50 0.43 0.57
420_31 12 0.45 0.38 0.51
680_28 13 0.46 0.39 0.53
680_31 12 0.40 0.34 0.47
(b) PSTR
300_28 16 0.53 0.47 0.59
300_31 9 0.27 0.19 0.35
3300_28 16 0.43 0.36 0.49
3300_31 8 0.17 0.09 0.24
420_28 5 0.49 0.42 0.56
420_31 6 0.23 0.15 0.32
680_28 14 0.45 0.39 0.51
680_31 5 0.19 0.11 0.28
(c) PAST
300_28 11 0.23 0.17 0.30
300_31 6 0.19 0.10 0.27
3300_28 12 0.13 0.06 0.20
3300_31 4 0.08 0.00 0.17
420_28 12 0.20 0.13 0.26
420_31 7 0.15 0.07 0.23
680_28 10 0.16 0.09 0.22
680_31 9 0.11 0.03 0.19
Table 1. T90 modeled mean coral host lipid content and 95% confidence intervals for each species
treatment N mean lower 95% upper 95%
(a) SSID
300_28 11 0.37 0.30 0.44
300_31 9 0.35 0.28 0.42
3300_28 12 0.37 0.30 0.44
3300_31 12 0.35 0.28 0.42
420_28 12 0.37 0.30 0.44
420_31 12 0.35 0.27 0.42
680_28 13 0.38 0.31 0.45
680_31 12 0.36 0.29 0.43
(b) PSTR
300_28 16 0.24 0.17 0.31
300_31 9 0.11 0.02 0.20
3300_28 15 0.24 0.17 0.31
3300_31 8 0.10 0.02 0.19
420_28 5 0.24 0.17 0.31
420_31 5 0.11 0.02 0.20
680_28 14 0.24 0.17 0.31
680_31 5 0.11 0.02 0.20
(c) PAST
300_28 11 0.15 0.08 0.23
300_31 6 0.20 0.11 0.29
3300_28 12 0.16 0.08 0.23
3300_31 4 0.22 0.14 0.31
420_28 12 0.16 0.08 0.23
420_31 7 0.20 0.11 0.29
680_28 10 0.16 0.08 0.23
680_31 9 0.20 0.11 0.29
Table 1. T90 modeled mean coral host carbohydrate content and 95% confidence intervals for each species
treatment N mean lower 95% upper 95%
(a) SSID
300_28 11 1.15 0.95 1.35
300_31 8 0.82 0.61 1.02
3300_28 12 1.10 0.91 1.29
3300_31 12 0.77 0.60 0.96
420_28 12 1.08 0.90 1.26
420_31 12 0.75 0.57 0.94
680_28 13 1.27 1.10 1.45
680_31 12 0.94 0.75 1.11
(b) PSTR
300_28 16 0.77 0.60 0.93
300_31 9 0.50 0.30 0.68
3300_28 16 0.62 0.45 0.78
3300_31 8 0.34 0.15 0.55
420_28 5 0.67 0.41 0.92
420_31 6 0.40 0.16 0.65
680_28 14 0.56 0.37 0.75
680_31 7 0.29 0.07 0.51
(c) PAST
300_28 11 0.82 0.61 1.03
300_31 6 0.65 0.41 0.88
3300_28 12 0.58 0.38 0.78
3300_31 4 0.41 0.16 0.65
420_28 12 0.90 0.71 1.10
420_31 7 0.73 0.51 0.95
680_28 10 0.61 0.41 0.81
680_31 9 0.43 0.23 0.64
Table 1. T90 modeled mean coral symbiont density content and 95% confidence intervals for each species
treatment N mean lower 95% upper 95%
(a) SSID
300_28 11 3.32 2.23 4.46
300_31 9 2.45 1.33 3.58
3300_28 12 2.04 0.97 3.07
3300_31 12 1.18 0.12 2.23
420_28 12 3.48 2.42 4.50
420_31 12 2.61 1.55 3.67
680_28 13 2.96 1.95 3.98
680_31 12 2.10 1.04 3.14
(b) PSTR
300_28 16 2.16 1.14 3.15
300_31 9 0.42 -0.77 1.60
3300_28 16 1.53 0.53 2.52
3300_31 8 -0.27 -1.48 0.89
420_28 5 2.16 0.75 3.61
420_31 6 0.45 -0.96 1.86
680_28 14 1.71 0.68 2.75
680_31 7 -0.09 -1.30 1.14
(c) PAST
300_28 11 7.29 6.13 8.48
300_31 6 6.42 5.02 7.74
3300_28 12 5.92 4.74 7.16
3300_31 4 4.86 3.51 6.15
420_28 12 6.43 5.28 7.57
420_31 6 5.51 4.22 6.83
680_28 10 5.09 3.84 6.35
680_31 8 4.19 2.87 5.45
Table 1. T90 modeled mean coral symbiont chlorophyll a content and 95% confidence intervals for each species
treatment N mean lower 95% upper 95%
(a) SSID
300_28 11 112.38 81.74 143.62
300_31 9 105.47 71.18 140.02
3300_28 12 48.52 17.15 79.21
3300_31 12 32.61 3.07 63.16
420_28 12 155.21 122.77 186.81
420_31 12 77.84 46.62 108.58
680_28 13 83.24 53.49 114.40
680_31 12 82.41 51.78 113.66
(b) PSTR
300_28 16 185.93 157.24 214.55
300_31 9 120.37 85.65 154.64
3300_28 16 78.53 51.36 106.93
3300_31 8 -1.42 -37.11 34.23
420_28 5 161.17 118.71 202.49
420_31 6 26.74 -14.58 66.79
680_28 14 84.10 54.62 114.41
680_31 5 17.96 -22.30 58.03
(c) PAST
300_28 11 97.02 63.84 130.54
300_31 6 155.01 116.85 192.29
3300_28 12 15.56 -18.42 45.96
3300_31 4 61.04 19.29 101.45
420_28 12 64.66 33.23 97.25
420_31 7 51.82 15.19 89.83
680_28 10 33.69 1.31 67.61
680_31 9 96.83 62.24 133.28
Table 1. T90 modeled mean coral host energy reserves and 95% confidence intervals for each species
treatment N mean lower 95% upper 95%
(a) SSID
300_28 11 2.02 1.61 2.43
300_31 8 1.62 1.21 2.04
3300_28 12 1.92 1.56 2.28
3300_31 12 1.53 1.17 1.89
420_28 12 2.02 1.65 2.40
420_31 12 1.58 1.21 1.95
680_28 13 2.06 1.70 2.41
680_31 12 1.65 1.29 2.01
(b) PSTR
300_28 16 1.60 1.25 1.94
300_31 9 0.96 0.58 1.35
3300_28 15 1.28 0.92 1.64
3300_31 8 0.60 0.20 0.99
420_28 5 1.39 0.84 1.94
420_31 5 0.71 0.14 1.27
680_28 14 1.23 0.82 1.62
680_31 5 0.56 0.11 1.00
(c) PAST
300_28 11 1.26 0.84 1.69
300_31 6 1.12 0.65 1.60
3300_28 12 0.86 0.41 1.29
3300_31 4 0.56 0.13 0.98
420_28 12 1.26 0.86 1.66
420_31 7 1.14 0.71 1.58
680_28 10 0.85 0.44 1.25
680_31 9 0.72 0.31 1.14


Session information

Session information from the last run date on 2021-04-23:

## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS High Sierra 10.13.6
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] png_0.1-7          MASS_7.3-53.1      performance_0.7.1  wesanderson_0.3.6 
##  [5] RColorBrewer_1.1-2 gridGraphics_0.5-1 corrplot_0.84      Hmisc_4.5-0       
##  [9] Formula_1.2-4      survival_3.2-10    magick_2.7.1       ggpubr_0.4.0      
## [13] vroom_1.4.0        lmerTest_3.1-3     lme4_1.1-26        Matrix_1.3-2      
## [17] kableExtra_1.3.4   ggfortify_0.4.11   cowplot_1.1.1      Rmisc_1.5         
## [21] shiny_1.6.0        vegan_2.5-7        lattice_0.20-41    permute_0.9-5     
## [25] forcats_0.5.1      stringr_1.4.0      purrr_0.3.4        tibble_3.1.0      
## [29] tidyverse_1.3.0    plotly_4.9.3       openxlsx_4.2.3     corrgram_1.13     
## [33] tidyr_1.1.3        ggbiplot_0.55      scales_1.1.1       plyr_1.8.6        
## [37] dplyr_1.0.5        ggplot2_3.3.3      readr_1.4.0        knitr_1.31        
## 
## loaded via a namespace (and not attached):
##   [1] readxl_1.3.1        backports_1.2.1     systemfonts_1.0.1  
##   [4] lazyeval_0.2.2      splines_3.6.3       digest_0.6.27      
##   [7] foreach_1.5.1       htmltools_0.5.1.1   fansi_0.4.2        
##  [10] magrittr_2.0.1      checkmate_2.0.0     cluster_2.1.1      
##  [13] see_0.6.3           modelr_0.1.8        svglite_2.0.0      
##  [16] jpeg_0.1-8.1        colorspace_2.0-0    ggrepel_0.9.1      
##  [19] rvest_1.0.0         haven_2.3.1         xfun_0.22          
##  [22] crayon_1.4.1        jsonlite_1.7.2      iterators_1.0.13   
##  [25] glue_1.4.2          registry_0.5-1      gtable_0.3.0       
##  [28] emmeans_1.5.5-1     webshot_0.5.2       car_3.0-10         
##  [31] abind_1.4-5         mvtnorm_1.1-1       DBI_1.1.1          
##  [34] rstatix_0.7.0       Rcpp_1.0.6          viridisLite_0.3.0  
##  [37] xtable_1.8-4        htmlTable_2.1.0     foreign_0.8-75     
##  [40] bit_4.0.4           htmlwidgets_1.5.3   httr_1.4.2         
##  [43] ellipsis_0.3.1      farver_2.1.0        pkgconfig_2.0.3    
##  [46] nnet_7.3-15         sass_0.3.1          dbplyr_2.1.1       
##  [49] utf8_1.2.1          effectsize_0.4.4-1  labeling_0.4.2     
##  [52] tidyselect_1.1.0    rlang_0.4.10        later_1.1.0.1      
##  [55] munsell_0.5.0       cellranger_1.1.0    tools_3.6.3        
##  [58] cli_2.4.0           generics_0.1.0      ggridges_0.5.3     
##  [61] broom_0.7.6         evaluate_0.14       fastmap_1.1.0      
##  [64] yaml_2.2.1          bit64_4.0.5         fs_1.5.0           
##  [67] zip_2.1.1           nlme_3.1-152        mime_0.10          
##  [70] xml2_1.3.2          compiler_3.6.3      rstudioapi_0.13    
##  [73] curl_4.3            ggsignif_0.6.1      reprex_2.0.0       
##  [76] statmod_1.4.35      bslib_0.2.4         stringi_1.5.3      
##  [79] parameters_0.13.0   highr_0.8           nloptr_1.2.2.2     
##  [82] vctrs_0.3.7         pillar_1.6.0        lifecycle_1.0.0    
##  [85] jquerylib_0.1.3     estimability_1.3    insight_0.13.2     
##  [88] data.table_1.14.0   seriation_1.2-9     httpuv_1.5.5       
##  [91] R6_2.5.0            latticeExtra_0.6-29 promises_1.2.0.1   
##  [94] TSP_1.1-10          gridExtra_2.3       rio_0.5.26         
##  [97] codetools_0.2-18    boot_1.3-27         assertthat_0.2.1   
## [100] withr_2.4.1         bayestestR_0.9.0    mgcv_1.8-34        
## [103] parallel_3.6.3      hms_1.0.0           rpart_4.1-15       
## [106] coda_0.19-4         minqa_1.2.4         rmarkdown_2.7      
## [109] carData_3.0-4       numDeriv_2016.8-1.1 lubridate_1.7.10   
## [112] base64enc_0.1-3